That rule of thumb is only approximate. Some people can hand-hold at slower speeds, and others only at faster speeds than the "rule" allows. Insofar as I know the rule was developed for smaller sized roll film and 35 mm cameras, and ought to apply to digitals. So, if you've got your zoom at 50 mm, 1/60 second is approximately the slowest shutter speed you should use. BUT if you're really steady, braced, and hold your breath, you might be able to hand-hold at 1/8 sec. Or not.
In general, you'll get sharper images of most objects by using higher shutter speeds. FWIW, when I was shooting a lot, I learned that using a tripod gave me crisper images, even when I was shooting at 1/125. But I'm a shaky old geezer.
"Keeping shooting will do more for the excellence of your photography than most any camera will!" JimmyD, PGS Extraordinaire.